Sato introduced the notion of growth constants, referred in the present paper as -order and -type , which are generalizations of concepts of classical order and type by defining

and if , then

for where and . Sato has also obtained the coefficient equivalents of and for the entire function when . It is noted that Sato's coefficient equivalents of , and also hold true for if 's are replaced by 's in his coefficient equivalents. Analogous to and lower -order and lower -type for entire function are introduced here by defining

and if then

For the case , these notions are due to Whittakar and Shah respectively. For the constant , two complete coefficient characterizations have been found which generalize the earlier known results. For coefficient characterization only for those entire functions for which the consecutive principal indices are asymptotic is obtained. Determination of a complete coefficient characterization of remains an open problem. Further -growth and lower -growth numbers for entire function we defined

for and . Earlier results of Juneja giving the coefficients characterization of and are extended and generalized. A new decomposition theorem for entire functions of -regular growth but not of perfectly -regular growth has been found.